Research Publications

Tight spans, Isbell completions and semitropical modules
Theory and Applications of Categories 28 (2013) 696732.
arxiv:1302.4370
[Blogpost]

On the magnitude of spheres, surfaces and other homogeneous spaces
Geometriae Dedicata (2013).
arxiv:1005.4041
[Blogpost]

On the asymptotic magnitude of subsets of Euclidean space (with Tom Leinster)
Geometriae Dedicata 164 (2013) 287310.
arxiv:0908.1582
[Blogpost]

The Mukai pairing, I: a categorical approach
(with A.Caldararu),
New York Journal of Mathematics 16 (2010) 6198.
arXiv:0707.2052

On the RozanskyWitten weight systems
(with J.Roberts),
Algebraic & Geometric Topology 10 (2010) 14551519. math.DG/0602653.
See also Justin Roberts' talk.

A diagrammatic approach to Hopf monads
[For less wide typesetting style see arXiv version.]
Arabian Journal of Science and Engineering C  Theme Issue "Interactions of algebraic and coalgebraic structures
(theory and applications)" December 2008; Vol. 33, Number 2C
math/0807.0658

The twisted Drinfeld double of a finite group via gerbes and finite groupoids
Algebraic & Geometric Topology 8 (2008) 14191457
math.QA/0503266

Gerbes and Homotopy Quantum Field Theories (with U.Bunke and P.Turner)
Algebr. Geom. Topol. 4 (2004) 407437
math/0201116

Homotopy quantum field
theories and related ideas (with M.Brightwell and P.Turner)
Int.
J. Modern Phys. A 18 Supplement (2003) 115122.

An almostintegral universal Vassiliev invariant of knots
Algebraic
and Geometric Topology 2 (2002) paper no. 29, 649664
math/0105190

On the first two Vassiliev invariants,
Experimental Mathematics
(2002).
 Free groups and finite type invariants
of pure braids (with J.Mostovoy)
Math. Proc. Camb. Phil. Soc. 132
(2001) 117130.

The Kontsevich integral and algebraic structures on the space of diagrams,
Knots in Hellas '98, Series on Knots and Everything vol 24, World Scientific,
2000, 530546.

Vassiliev invariants
as polynomials,
Knot Theory, Banach Centre Publications 42
(1998) 457463.

A combinatorial halfintegration from weight system to
Vassiliev knot invariant,
J. Knot Theory Ramifications, 7
no. 4 (1998) 519526.

Vassiliev invariants and the Hopf algebra of chord diagrams,
Math.
Proc. Camb. Phil. Soc., 119 (1996) 5565.
Unpublished
 On the Vassiliev invariants for knots and for pure braids,
(official abstract) Edinburgh University PhD Thesis,
July 1997. This contains material from the above papers together with
ideas on the relationship between Vassiliev invariants for pure braids
and de Rham homotopy theory.
 Vassiliev invariants for knots,
Essay for Part III of the Cambridge
Mathematical Tripos, May 1993. A survey of BarNatan's paper On the
Vassiliev knot invariants, which contained some additional work
of my own.
Selected writings at the nCategory Café
 Formal Concept Analysis
(Sep 2, 2013)
 Have a peek at the notion of formal concept analysis
 The Nucleus of a Profunctor: Some Categorified Linear Algebra
(Aug 19, 2013)
 Watch some linear algebra being categorified.
 Torsors and enriched categories
(Jun 3, 2013)
 Read about a different take on torsors
 Project Scheduling and Copresheaves
(Mar 24, 2013)
 Find out what PERT graphs have to do with enriched categories
 Tight spans, Isbell completions and semitropical modules
(Jan 20, 2013)
 See how these three things are related.
 The Spread of a Metric Space
(Sep 5, 2012)
 Read how this notion of size for metric spaces has some interesting properties.
 Integral Transforms and the PullPush Perspective, I
(Nov 7, 2010)
 Start to see how enriched profunctors can be viewed as categorifications of integral kernels.
 Enriching Over a Category of Subsets
(Aug 30, 2010)
 Discover how enriched category theory leads to the definition of some generalized metrics on the space of continuous functions on the unit interval.
 On the Magnitude of Spheres, Surfaces and Other Homogeneous Spaces
(Apr 21, 2010)
 See the details of a new paper on the magnitude of metric spaces.
 Modeling Surface Diagrams
(Mar 24, 2010)
 Watch some videos to see how I’m trying to make 3d models of categorical surface diagrams.
 Intrinsic Volumes and Weyl's Tube Formula
(Mar 12, 2010)
 Read about how the volume of a tube around a surface in 3space depends only on intrinsic invariants of the surface.
 A Look at the Mathematical Origins of Western Musical Scales
(Feb 26, 2010)
 See how the rational numbers 2 and 3/2 gave birth to the Western musical scale.
 More Magnitude of Metric Spaces and Problems with Penguins
(Oct 10, 2009)
 Learn about the tenuous link between emperor penguins and the magnitude of metric spaces.
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